I freeze leftover rice all the time. It's such a good treasure to have on hand. Stuff it into a ziplock bag, zip it locked, flatten out, and lay flat in the freezer. It takes up less space, and both freezes and thaws quickly.

I often freeze beans and whole grains. I place the well drained grains on a sheet pan and freeze. Then I break up the grains and put the loose frozen grain in a bag and back in the freezer. This way you can pour out just a bit and leave the rest in the freezer